Train from Paris to Arles

If you're willing to leave early, then I'd take the 7:40 direct train over the 8:37 departure with two connections. But most later departures only have one connection, which may be at Avignon TGV station (not going into Centre), or Nimes, or Marseille. Avignon Centre has bag storage but Avignon TGV does not.

If instead, I took the train from Paris to Avignon which would be 2
hours and 30 minutes we would have to change to the Center Ville
station in Avignon and then take a 20 minute train to Arles.

If you check the train schedules Paris to Avignon (then Avignon Centre to Arles) vs. Paris to Arles, it will take you around the same time; once you add the connection time at Avignon TGV (to get to Avignon Centre station) and then the connection time for the train traveling to Arles.

• BTW, there is no left luggage at either of the Avignon train stations.

Edit to add...

I'd forgotten that there is a left luggage office in downtown Avignon not far from the Avignon Centre train station.
Make sure to check their hours as they are closed on Sundays (September-- May)

If your final destination is Arles, you might think about taking the train from Paris to Avignon, then changing and going straight to Arles. This is especially true if you are coming off a trans-Atlantic flight.
Then, if you want to go to Avignon, after that - and baggage-free - you can do that in 20 mins.

Chexbres makes a good point.

It's so much better to visit a place without having to worry about luggage.

We visited Arles, from Avignon and it was an easy 20 minute train ride.

If you're planning to travel to other cities/towns in Provence via public transportation, Avignon is a good transportation hub.

Enjoy!

If you plan to rent a car, Avignon TGV has several agencies.